A drawer contains 4 red socks and 4 Question

Question

A drawer contains 4 red socks and 4 blue socks, all unmatching and mixed in total darkness. What is the minimum number of socks you must pull out to be 100% sure that you have at least one matching pair of any color?

Answer

this problem is solved using pigeonhole principle in the attached file. please feel free to ask if you can't understand.

Answer

the first pull results in either a red (r) or blue (b) sock.
the second pull will also result in either a red or blue sock. now consider our possibilities from the last pull:   
(a) if we pull red sock the possibilities are: rr, br.   (b) if we pull blue sock the possibilities are: rb, bb.
therefore, the possibilities after second pull are: rr, br, rb and bb socks. we see that 2 out of 4 possibilities have not given us a pair. hence, we cannot be 100% sure that the second pull has at least one matching pair of any colour.
  
the third pull will again result in either a red or blue sock. now consider our possibilities from the previous pull:   (c) if we pull red sock the possibilities are: rrr, brr, rbr, bbr.(d) if we pull blue sock the possibilities are: rrb, brb, rbb, bbb.
regardless of whether the third pull result in red or blue sock, we got a complete pair of either red socks or blue socks.
  
hence, we must pull out a minimum of 3 socks to be 100% sure to have at least one matching pair.

Answer

Answer

the minimum number of socks you must pull out is 3.
explanation:
since there are only 2 colors (red and blue), if you pick 2 socks, the worst-case scenario is that you get 1 red and 1 blue sock.
when you pull out a 3rd sock, it must match one of the first two colors. according to the pigeonhole principle, pulling out 3 socks guarantees at least one matching pair of the same color.

Answer

the minimum number is 3 socks.here’s the simple logic (pigeonhole principle):· there are only 2 colors (red and blue).· if you pull out 2 socks, they could be one red and one blue&mdash;so you might not have a match.· if you pull out 3 socks, even in the worst-case scenario, two of them must share the same color because there are only two color options available.so, with 3 socks, you are 100% guaranteed to have at least one matching pair.

Answer

Answer

1) there are 2 colors of socks (red and blue)2) when 2 socks are pulled out, there are 2 possibilities :i. both the socks are of one matching pair of any color (red or blue)ii. both the socks are of different colors (one is red and other is blue)as it is not to be a 100% sure chance, next step is to be carried out:3) when a 3rd sock is pulled out, it must be either red or blue. no matter which color it is, it will perfectly match one of the first two socks you already drew.conclusion :the minimum number of 3 socks  must pull out to be 100% sure that there is at least one matching pair of any color.

Answer

explanationto find the minimum number needed to be 100% sure, look at the worst-case scenario using the pigeonhole principle:pull 1: you might pull a red sock.pull 2: you might pull a blue sock. (at this point, you have one of each color and no pair yet).pull 3: because there are only two colors in total, your third sock must be either red or blue, completing a pair with one of the first two socks.

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A drawer contains 4 red socks and 4 Question

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